As one example of the inertia sensor, the accelerometer which is well known may be cited. It is generally a one-axis accelerometer which is furnished with one sensitive axis. When this one-axis accelerometer is calibrated, the calibration is effected by causing the direction of motion generated by a motion generating machine to coincide with the axis of sensitivity. The degree of freedom of motion to be used for calibrating accelerometers, therefore, is a single degree of freedom. The primary calibration using a laser interferometer which is reputed to have the highest precision also uses this technique.
However, since the device which calibrates the one-axis accelerometer mentioned above generally entails a three-dimensional motion, it is rare that the device will be limited to a one-dimensional motion. The fact that the calibration is carried out by causing the direction of motion generated by the motion generating machine to coincide with the axis of sensitivity as described above occurs in the calibration which resorts to the measurement of the amplitude of the acceleration when the direction of motion is known in advance.
The “motion generating machine” used herein is a machine normally called a vibration table that generates translational motion with one degree of freedom. But, here in this application motion generating machine is a machine that generates motion with more than one degree of freedom including both translational and rotational motions.
As concrete examples of the conventional one-axis accelerometer, a piezoelectric type accelerometer, an electromagnetic type servo accelerometer, an interference type optical fiber accelerometer and a strain gauge type accelerometer have been known. Owing to their structures and the natures of their materials, accelerometers are influenced by the acceleration components not parallel to the sensitivity axis when the directions of application of acceleration to the acceleration sensors fail to coincide with the direction of sensitivity axis.
It is, therefore, apparent that concerning practical motions, the calibration technique alone in the present state of affairs has not fully satisfactorily established a method for evaluating the performance of an acceleration sensor or perfected a measurement standard for the determination of acceleration.
It is derived that in terms of vector space with three-dimensional transverse motion, even the cross or transverse sensitivities of one-axis accelerometers are expressed by two parameters as will be subsequently explained. The practice of denoting the two kinds of transverse sensitivity by Sz,x and Sz,y and designating Sz,x as a magnitude of not more than 5% and Sz,y as a magnitude of not more than 3% has never been in vogue heretofore.
It is natural that the one-axis accelerometer generally emits an output signal in response to an input component in the direction of the sensitivity axis thereof. It is also characterized by emitting output signals in response to input acceleration components from two directions perpendicular to the sensitivity axis thereof. The reason for this property is that the piezoelectric accelerometer, the electromagnetic servo accelerometer, the interferometer type optical fiber accelerometer, or the strain gauge type accelerometer mentioned above is provided with a mass capable of also moving, though slightly, in a direction other than the direction of sensitivity axis or something equivalent thereto and, therefore, is so configured as to detect the relative motion of this mass or detect a voltage or an electric current necessary for preventing this relative motion.
Heretofore, the accelerometer is set on the one-axis motion generating machine and the sensitivity axis of the accelerometer is caused to coincide with the direction of the motion generated by a vibration table (motion generating machine) as illustrated in FIG. 3. The concept of enabling the accelerometer to be calibrated most accurately by measuring a motion with a laser interferometer under such set conditions as mentioned above and consequently establishing a standard for measurement of acceleration is officially approved by the Treaty of the Meter as well. Generally, the reference accelerometer is calibrated in accordance with the method embodying this concept.
Then, in industries, it is supposed to calibrate a given accelerometer based on a reference accelerometer mentioned above by joining in series connection the reference accelerometer which has undergone measurement by the method of FIG. 3 and the given accelerometer as illustrated in FIG. 4(b), causing the sensitivity axis to coincide with the direction of motion generated by a motion generating machine, and comparing the output signals from the two accelerometers.
The conventional method of calibration which resides in determining the transverse sensitivity from the output signal due to a motion only in one direction perpendicular to the sensitivity axis as illustrated in FIG. 4(a) and FIG. 4(b), however, is essentially in error in the elementary sense. In the sense that this method is an expedient and is capable of determining only one transverse-sensitivity, the thought directed toward the decomposition and the synthesis of vector supports a judgment that this method views the phenomenon only in a two-dimensional space.
The transverse sensitivity is determined by imparting vibration only in one direction perpendicular to the sensitivity axis as illustrated in FIG. 4(c).
For the sake of surveying the transverse sensitivity more specifically, the behavior of the piezoelectric type accelerometer using a piezoelectric material, for example, will be explained below. The piezoelectric type accelerometer possesses transverse sensitivity because the piezoelectric constant comprises a shear component. That is, the piezoelectric substance generates an electric charge which transmits a signal via an electrode even to slippage. Generally, in the region in which the voltage (or electric current) generated in response to an input signal (acceleration) possesses linearity, the sensor sensitivity is defined by the ratio of their magnitudes. Thus, the following formula is established.
                                                                        The  sensitivity  axis  output  voltage                                                                                                          (                                                                                    a                        ox                                            ⁡                                              (                        ω                        )                                                              ⁢                                          exp                      ⁡                                              (                                                  j                          ⁢                                                                                                          ⁢                          ω                          ⁢                                                                                                          ⁢                          t                                                )                                                                              )                                ⁢                                                                  ⁢                of                ⁢                                                                  ⁢                accelerometer                                                    =                ⁢                  normal          ⁢                                          ⁢          sensitivity          ×                                                ⁢                  input          ⁢                                          ⁢          component          ⁢                                          ⁢          of          ⁢                                          ⁢          acceleration                                                ⁢                              in            ⁢                                                  ⁢            normal            ⁢                                                  ⁢            sensitivity            ⁢                                                  ⁢            direction                    +                                                ⁢                  cross          ⁢                                          ⁢                      (            transverse            )                    ⁢                                          ⁢          sensitivity          ⁢                                          ⁢          1          ×                                                ⁢                  input          ⁢                                          ⁢          component          ⁢                                          ⁢          of          ⁢                                          ⁢          acceleration                                                ⁢                  in          ⁢                                          ⁢          direction          ⁢                                          ⁢          1          ⁢                                          ⁢          perpendicular                                                ⁢                              to            ⁢                                                  ⁢            normal                    +                      cross            ⁢                                                  ⁢                          (              transverse              )                                                                      ⁢                  sensitivity          ⁢                                          ⁢          2          ×          input          ⁢                                          ⁢          component                                                ⁢                  of          ⁢                                          ⁢          acceleration          ⁢                                          ⁢          in          ⁢                                          ⁢          direction          ⁢                                          ⁢          2                                                ⁢                  perpendicular          ⁢                                          ⁢          to          ⁢                                          ⁢          main          ⁢                                          ⁢          axis                                        =                ⁢                                                            S                                  x                  ,                  x                                            ⁡                              (                ω                )                                      ⁢                          a              ix                        ⁢                          exp              ⁡                              (                                  j                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                )                                              +                                                ⁢                                            S                              x                ,                y                                      ⁢                          a              iy                        ⁢                          exp              ⁡                              (                                  j                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                )                                              +                                    S                              x                ,                z                                      ⁢                          a              iz                        ⁢                          exp              ⁡                              (                                  j                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                )                                                        
When this formula is rewritten in the matrix form, the formula 1 is obtained. Here, the amplitude of the vector acceleration exerted on the accelerometer is denoted by (aix, aiy, aiz) and the time change component by exp(jωt).
                                                        a              ox                        ⁡                          (              ω              )                                ⁢                      exp            ⁡                          (                              j                ⁢                                                                  ⁢                ω                ⁢                                                                  ⁢                t                            )                                      =                              (                                                            S                                      x                    ,                    x                                                  ⁡                                  (                  ω                  )                                            ,                                                S                                      x                    ,                    y                                                  ⁡                                  (                  ω                  )                                            ,                                                S                                      x                    ,                    z                                                  ⁡                                  (                  ω                  )                                                      )                    ⁢                      (                                                                                                                                                                                    a                            ix                                                    ⁢                                                      exp                            ⁡                                                          (                                                              j                                ⁢                                                                                                                                  ⁢                                ω                                ⁢                                                                                                                                  ⁢                                t                                                            )                                                                                                                                                                                                                                                a                            iy                                                    ⁢                                                      exp                            ⁡                                                          (                                                              j                                ⁢                                                                                                                                  ⁢                                ω                                ⁢                                                                                                                                  ⁢                                t                                                            )                                                                                                                                                                                                                                                                  a                      iz                                        ⁢                                          exp                      ⁡                                              (                                                  j                          ⁢                                                                                                          ⁢                          ω                          ⁢                                                                                                          ⁢                          t                                                )                                                                                                                  )                                              (                  Mathematical          ⁢                                          ⁢          1                )            
The drawing of the acceleration vector A applied to the accelerometer and the decomposition of the vector in X, Y and Z axes is shown in FIG. 2.
It is well known that the acceleration is a vector which is expressed by amplitude and direction. Further, in order that the accelerometer may correctly measure the acceleration, the accelerometer must be calibrated with the acceleration as a vector. The conventional method of calibration, however, effects the calibration with the magnitude of amplitude because the direction of the exerted acceleration is determined at the stage of setup.
When the accelerometer is put to actual services, there are times when the direction of motion can be forecast and there are times when the forecast cannot be attained because of the possibility of the accelerator being exposed to application of acceleration in every direction.
In the case of an earthquake or accidental collision of cars, it is not possible to know in advance the direction of motion. When the calibration is made only in amplitude (one-dimensionally) as practiced conventionally, there are times when no correct magnitude of acceleration can be obtained. Thus, the desirability of calibrating the accelerometer by applying acceleration to the accelerometer in all actually conceivable directions has been finding general recognition.
The technical background of this invention has been described heretofore. As concrete examples of the prior art of this invention, the following documents have been known.
[Non-Patent Document 1] Vibration Engineering Handbook, complied by Osamu Taniguchi, published in 1976 by Youkendo, Chapter 13 “Determination of Vibration,” 13.3.2 “Calibration of vibration measuring device” (in Japanese)
[Non-Patent Document 2] ISO (the International Organization for Standardization) 16063-11: 1999 (E) Methods for the calibration of vibration and shock transducers Part 11: Primary vibration calibration by laser interferometer
[Non-Patent Document 3] FINAL REPORT ON KEY COMPARISON CCAUV. V-K1 Hans-Jurgen von Martens, Clemens Elster, Alfred Link, Angelika Taubner, Wolfgang Wabinski, PTB-1.22 Braunschweig, Oct. 1, 2002
[Non-Patent Document 4] ISO 5347 Methods for the calibration of vibration and shock pick-ups: part 11 Testing of transverse vibration sensitivity
[Non-Patent Document 5] ISO 5347 Methods for the calibration of vibration and shock pick-ups: part 12 Testing of transverse shock sensitivity
[Non-Patent Document 6] ISO 8041 Human response to vibration—Measuring instrumentation
[Non-Patent Document 7] ISO 2631-1, 1997 Evaluation of human exposure to whole-body vibration Part 1: General requirement
[Non-Patent Document 8] ISO 5349-1, 2001 Measurement and evaluation of human exposure to hand-transmitted vibration—Part 1: General guidelines